Boolean Modifyer dissapears if I delete object
Blender keeps data of all modifier in temporary state until the modifier is applied. Simply putting at this stage you can do whatever you want with modifiers. So, blender is not sure at this point. You can delete the modifier and object will return back to it's base form. So, modifier data and object data are dependent to each other. If one is affected then other one will be affected too.
Coming to your scenario, Assume there is a cylinder going through the cube. Boolean modifier is configured to affect the cube. So, if cylinder is going through the cube it will make a hole in cube. When you delete the cylinder you will loose hole too. Because object data and cylinder data are dependent to each other. So, to save your hole apply the modifier. This will now make modifier data independent to modifier object and your target object will be modified. After you can delete the modifier object. in this case after applying modifier you can delete cylinder and you will have hole in cube.